We can write a quadratic equation in factored form using the given roots. Then we will rewrite it in standard form by multiplying the factors.
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Factored Form:& a(x-p)(x-q)=0
Standard Form:& ax^2+bx+c=0
In the factored form, p and q are the roots of the equation. Since we are told the roots are - 6 and 14, we can partially write the factored form of our equation.
a( x-( - 6 ) ) ( x-1/4 )=0
⇕
a( x+ 6 ) ( x-1/4 )=0
Since a does not have any effect on the roots, we can choose any value. For simplicity and in order to have integercoefficients, we will let a=4. This will allow us to eliminate the fractional part when we distribute.
4( x+ 6) ( x-1/4 )=0
Finally, let's use the Distributive Property to obtain the standard form.
